Cardiac computational models of electrical conduction, mechanical activation, hemodynamics and metabolism require detailed information about the structural arrangement of functionally heterogeneous cardiac cell types. However, current state-of-the-art models lack anatomically accurate cell type localization, which limits their utility. Histological sections combine unique resolution with discrimination of tissues and anatomical structures, but they suffer from alignment and deformation problems. On the other hand, MRI datasets preserve the correct geometry, but provide less micro structural detail. This paper presents a method for aligning MRI and histological datasets to obtain a highly detailed, geometrically correct anatomical description of the heart. An iterative process is used to correct the various 2D and 3D, rigid and non-rigid transforms, introduced in the histology preparation and acquisition. Validation is performed by calculating distances between anatomical landmarks in ...